I recently dived into the YouTube javascript API as we (the company I work for) wanted to track behaviour on the video (note that the YouTube javascript API is not great for this task, but that is another matter).
However, we encountered a strange issue where the fullscreen button was greyed out and was not clickable despite we included the fs=1 parameter in the embed URL.
The fix is simple, but subtle. You remember how the embed codes included those <param> tags that did some magical work which you never cared to remember? When I used an example found on the YouTube API reference they did not include the fullscreen parameter required to make fullscreen mode work.
Example (for a full working example see the code at the YouTube javascript API page):
From the example below you can see we must add the allowFullScreen parameter to the parameter list. This should enable you to view the video in fullscreen.
(function() { var params = { allowScriptAccess: "always", <strong>allowFullScreen: "true"</strong> }, atts = { id: "myid" }; swfobject.embedSWF("https://www.youtube.com/v/VIDEO_ID?version=3&feature=player_embedded&fs=1 &enablejsapi=1&playerapiid=myid", "ytapiplayer", "340", "191", "8", null, null, params, atts); })()